How do I backup my iPhone with iCloud?
Apple's iCloud servers will automatically back up your iOS device, assuming that iCloud Backup is enabled. To enable iCloud navigate to Settings -> iCloud -> Backup & Storage.
The backup runs automatically every day when your device is:
Connected to the Internet via Wi-Fi
Connected to your charger
Your device screen is locked
You can back up with iCloud manually if you are connected to a Wi-Fi network by selecting Settings -> iCloud -> Storage & Backup -> Back Up Now.
iTunes has a nasty habit of deleting the previous backup every time it does a backup. If you really have an old backup intact, there is a way to restore from it. I forget the procedure, but I'm sure you can Google it. It's a good idea to manually go into your backup directory and manually copy it over to a new name once in a while. That way iTunes won't touch it, and you can use it in an emergency such as yours.
Here's a website that describes how to do it:
ipadconverter-mac.com/mac-iphone-data-recovery/